{
  "id": "2401.05829",
  "version": "v1",
  "published": "2024-01-11T10:54:29.000Z",
  "updated": "2024-01-11T10:54:29.000Z",
  "title": "Asymptotic behavior for fully nonlinear elliptic equations in exterior domains",
  "authors": [
    "Lian Yuanyuan",
    "Zhang Kai"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we obtain the asymptotic behavior at infinity for viscosity solutions of fully nonlinear elliptic equations in exterior domains. We show that if the solution $u$ grows linearly, there exists a linear polynomial $P$ such that $u-P$ is controlled by fundamental solutions of the Pucci's operators. In addition, with proper ellipticity constants, $u(x)-P(x)\\to 0$ as $x\\to \\infty$ (see Theorem 1.11). If $u$ grows quadratically, we obtain similar asymptotic behavior (see Theorem 1.16). In this paper, we don't require any smoothness of the fully nonlinear operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-11T10:54:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B53",
      "35J15",
      "35J60",
      "35D40"
    ],
    "keywords": [
      "fully nonlinear elliptic equations",
      "exterior domains",
      "similar asymptotic behavior",
      "proper ellipticity constants",
      "viscosity solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}